In recent years, improved nuclear magnetic well logging devices and techniques have been proposed and/or developed. A summary of these devices and techniques is presented in U.S. Pat. No. 5,023,551. The referenced '551 Patent also reviews basic principles of NMR and NMR logging, and part of that review will be summarized. Reference can be made to the '551 Patent for further detail.
NMR has been a common laboratory technique for forty years, and a theoretical description is available in Abragam, Principles of Nuclear Magnetism, Clarendon Press (Oxford, 1961), and Farrar and Becker, Pulse and Fourier Transform NMR, Academic Press (New York 1971). NMR is based on the fact that the nuclei of many elements have angular momentum ("spin") and a magnetic moment. The nuclear spins align themselves along an externally applied static magnetic field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins away from the static field direction. The angle through which the spins are tipped is under the control of the experimenter, as explained below.
After tipping, two things occur simultaneously. First, the spins precess around the static field at a particular frequency (i.e. the Larmor frequency), given by .omega..sub.0 =.gamma.B.sub.0, where B.sub.0 is the strength of the static field and .gamma. is the gyromagnetic ratio, a nuclear constant. Second, the spins return to the equilibrium direction according to a decay time known as the "spin lattice relaxation time" or T1. For hydrogen nuclei, .gamma./2.pi.=4258 Hz/Gauss, so for a static field of 235 Gauss, the frequency of precession is 1 MHz. T1 is controlled totally by the molecular environment and is typically ten to one thousand milliseconds in rocks.
Also associated with the spin of molecular nuclei is a second relaxation time known as the "spin-spin relaxation time", or T2. At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field, and they all precess at the Larmor frequency. However, because of small inhomogeneities in the static field due to imperfect instrumentation or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time that is long compared to the precession period, but shorter than T1, the spins will no longer be precessing in unison. When this "dephasing" is due to static field inhomogeneity of the apparatus, the dephasing is sometimes called T2*. When it is due to properties of the material, the dephasing time is called T2. T2 and T2* can be measured independently. For liquids in rocks, T2 is approximately two-thirds of T1.
As aforementioned, the parameters T1 and T2 are sensitive to molecular environment. For example, T2 can be several seconds in an unconfined low viscosity liquid such as water, while it can be as short as ten microseconds in a solid. Liquids confined in the pores of rocks present an intermediate case with T2 in the range of tens to hundreds of milliseconds, depending on pore size and fluid viscosity.
In the basic NMR measurement, a pulse of oscillating field is applied to the sample to tip the spins of the nuclei in the sample. The angle (in radians) through which the spins are tipped is given by the equation EQU .theta.=.gamma.B.sub.1 t.sub.p /2 (1)
where .gamma. is the gyromagnetic ratio, B.sub.1 is the linearly polarized oscillating field strength, and t.sub.p is the duration of the pulse. Tipping pulses of ninety and one hundred and eighty degrees are the most common.
The precessing spins are detected by voltage induced in a coil. Only that component of the nuclear magnetization that is precessing in the plane perpendicular to the static field can be sensed by the coil. Hence, a signal will be generated after a ninety degree tipping pulse but not after a one hundred eighty degree tipping pulse. In fact, after a one hundred eighty degree tipping pulse, the spins do not precess at all, but just slowly return along the B.sub.0 axis to the equilibrium direction.
In measuring the spin-lattice relaxation time T1, many different techniques are known both in the material science arts and in the medical arts. The "inversion recovery" technique suggests that after the nuclei have aligned themselves along the static magnetic field, a one hundred eighty degree pulse is applied to reverse the direction of the spins. Over time, the spins decay toward their equilibrium direction according to T1, but no measurement is yet made as the one hundred eighty degree pulse does not induce a signal in the coil. Before the decay is complete, however, it is interrupted by a ninety degree pulse which rotates the spins into the measurement plane (i.e. induces a signal in the coil). However, the measurable signal lasts only as long as the spins precess in unison. As they dephase, the net magnetization decreases, even if all the spins remain in the transverse plane. Therefore, the signal decays exponentially with time constant T2*, also known as the "free induction decay". Fortunately, the information of interest is the amplitude of the signal immediately after the ninety degree "read out" pulse. This amplitude depends on the "recovery time" (.tau.) between the original one hundred eighty degree pulse and the ninety degree pulse. Following a determination of amplitude, the spin system is permitted to completely relax back to equilibrium, and the pulse sequence is then repeated preferably numerous times with different recovery times. The detected amplitudes are then plotted against .tau. with the decay typically being expressed as a single exponential.
The inversion recovery technique for measuring T1 has been used in laboratories for about forty years. It is very time consuming, and therefore undesirable for well logging and other material property investigations. To overcome some of the shortcomings of inversion recovery, other techniques such as preparation recovery, steady state, and magnetization conserving techniques have been developed. Reference can be made to the above noted U.S. Pat. No. 5,023,551.
While many different methods for measuring T1 have been developed, a single standard known as the CPMG sequence (Carr-Purcell-Meiboom-Gill) for measuring T2 has evolved. In solids, where T2 is very short, T2 can be determined from the decay of the free induction signal. In liquids, where T2*&lt;&lt;T2, the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T2 in such situations, it is necessary to cancel the effect of the apparatus-induced inhomogeneities. To accomplish the same, a series of pulses is applied. First a ninety degree pulse causes the spins to start precessing. Then a one hundred eighty degree pulse is applied to keep the spins in the measurement plane, but to cause the spins which are dispersing in the transverse plane to reverse direction and to refocus. By repeatedly reversing the spins using one hundred eighty degree pulses, a series of "spin echoes" appear. This succession of one hundred eighty degree pulses after an initial ninety degree pulse is the Carr-Purcell sequence which measures the irreversible dephasing (i.e. T2) due to material properties.
While the Carr-Purcell sequence would appear to provide a solution to eliminating apparatus induced inhomogeneities, it was found by Meiboom and Gill that if the one hundred eighty degree pulses in the Carr-Purcell sequence were slightly misset, the transverse magnetization would steadily be rotated out of the transverse plane. As a result, substantial errors would enter the T2 determination. Meiboom and Gill devised a modification to the Carr-Purcell pulse sequence such that after the spins are tipped by ninety degrees and start to dephase, the carrier of the one hundred eighty degree pulses is phase shifted relative to the carrier of the ninety degree pulse. As a result, any error that occurs during an even pulse of the CPMG sequence is cancelled out by an opposing error in the odd pulse.
Identification of the presence of gas in a formation is one of the most important tasks of petrophysical log interpretation. Since NMR is a proton measurement, it is somewhat analogous to the porosity measurement with the neutron tool: it is sensitive to the hydrogen index of the formation, which is significantly reduced in gas. However, unlike the neutron tool, the NMR measurement is insensitive to neutron absorbers, crystalline waters of hydration, and clay bound water. A so-called "Amplitude Method" takes advantage of this to evaluate the gas volume of the formation. The Amplitude Method is summarized, for example, in Flaum, C., Kleinberg, R., and Hurlimann, M., Identification Of Gas With The Combinable Magnetic Resonance Tool (CMR), Paper L. SPWLA, 37th Annual Logging Symposium, New Orleans, Jun. 16-19, 1996.
Recently, much attention has been focused on a secondary phenomenon which can be exploited to use NMR for an independent indication of gas: diffusion.
Exploitation of the diffusion process is based on the fact that molecular diffusion is more rapid in gas than in water or most liquid hydrocarbons.
Diffusion can have a significant effect on the pulsed NMR measurement, since a diffusing molecule with a polarized proton can be displaced an appreciable distance between successive pulses. If the static magnetic field is not uniform, this displacement will cause a dephasing of the transverse magnetization. The result is a noticeable decrease in the relaxation time T.sub.2, or a shift in the T.sub.2 distribution spectrum to shorter times.
An additional feature of the NMR measurement is that the effect of diffusion depends on the echo spacing. Thus, by varying the echo spacing, the diffusion process can be observed and quantified.
Akkurt, et al. have taken advantage of this phenomenon to propose a qualitative gas detection method, which they call the "shifted spectrum" method. They take two separate measurements of T.sub.2 distribution, at two widely differing echo spacings, and present the difference between the two distributions in a waveform, or VDL display. [See Akkurt, R., Vinegar H. J., Tutunjian, P. N., and Guillory, A. J., 1995, NMR Logging Of Natural Gas Reservoirs, Paper N. SPWLA 36th Annual Logging Symposium, Paris.]
The drawback of the shifted spectrum method stems from the fact that it is quite sensitive to the details of the shapes of the individual T.sub.2 distribution spectra. In the absence of noise, where the observed shapes are truly representative of the formation behavior, the method would work well. In reality, the shape may be influenced by noise. This is because signal processing in the presence of noise broadens the T.sub.2 distributions. In the shifted spectrum method, the signal-to-noise ratio for the two passes can be quite different because the average signal power is much smaller for the longer echo spacing. Thus the difference between the spectra is influenced by the systematic effect of noise. This commonly results in a false positive indication.
A more quantitative approach for gas detection, which will be called the "echo difference" method, was proposed in Prammer, M. G., Mardon, D., Coates, G. R., and Miller, M. N., 1995, Lithology-Independent Gas Detection by Gradient-NMR Logging, SPE No. 30562, SPE 70th Annual Technical Conference, Dallas. An assumed gas diffusion coefficient is used to characterize the difference of echo decays at two different echo spacings. This difference is quantified as a function of oil and gas volumes, assuming that the two are non-wetting, i.e. that they exhibit single component T.sub.2 relaxation times, unaffected by the surface effects, and assuming knowledge of the diffusion coefficient of each phase.
A limitation of the echo difference method is that both the T.sub.2 and the diffusion coefficient of the gas are needed a priori. Diffusion, in particular, is hard to predict, as it depends not only on the bulk gas diffusion coefficient, but also on the degree of connectivity of the gas phase, since the diffusion process may occur over several pore diameters to show the effect of the field gradient. The gas connectivity, in turn, depends on clay content, pore tortuosity, and, to a large degree, on the gas saturation itself. Furthermore, echo difference can stand improvement in ruling out false gas indications.